Devices and methods for increasing energy and/or power density in composite flywheel energy storage systems

ABSTRACT

A flywheel formed of a composite material having fibers, oriented substantially in a circumferential direction around the flywheel, embedded in a matrix material. The flywheel having an inner surface, an outer surface, and a thickness therebetween and defining an axis of rotation. A plurality of load masses are distributed circumferentially on the inner surface at a longitudinal segment along the axis. A rotation of the flywheel about the axis with a rotational velocity generating hoop stress in the fibers in the circumferential direction and through-thickness stress is generated in the matrix material in a radial direction. Each load mass produces a force on the inner surface operative to reduce the maximum through-thickness stress in the matrix material as the flywheel rotates about the axis. The rotational velocity otherwise sufficient to produce structural failure of the matrix material produces structural failure of the fibers and not the matrix material.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/610,003, filed May 31, 2017, which is continuation of InternationalPatent Application No. PCT/US2015/063165 entitled “Devices and Methodsfor Increasing Energy and/or Power Density in Composite Flywheel EnergyStorage Systems,” filed Dec. 1, 2015, the disclosure of which isincorporated herein by reference in its entirety.

PCT/US2015/063165 is a continuation-in-part of U.S. patent applicationSer. No. 14/557,752, entitled “High Energy Density CompositeFlywheels/Electromechanical Batteries,” filed Dec. 2, 2014, thedisclosure of which is incorporated herein by reference in its entirety.

PCT/US2015/063165 is also a continuation-in-part of U.S. patentapplication Ser. No. 14/564,982, entitled “High Power DensityElectromechanical Energy Storage Flywheel,” filed Dec. 9, 2014, thedisclosure of which is incorporated herein by reference in its entirety.

BACKGROUND

Some embodiments described herein relate to electromagnetic machines andmore particularly to devices and methods for increasing energy and/orpower density in composite flywheel energy storage systems.

Electromechanical flywheel devices can be used for large capacity energystorage to improve, for example, the economic performance and stabilityof utility, industrial, military, and/or other suitable gridinfrastructures. Such flywheel devices are mechanical—storing energy viarotational kinetic energy and delivering energy back to the grid orlocal energized component via a motor/generator system at leastelectrically connected to the flywheel device. The application of someknown flywheel energy storage systems, however, can be limited based atleast in part on physical limitations associated with a mechanicalsystem (e.g., high forces associated with rotational velocities andacceleration, which can lead to failure of component materials and/orcatastrophic system failure and/or the like).

For example, it is usually desirable to maximize the energy density(energy per unit mass, W-h/kg). The kinetic energy associated with theflywheel can be increased (e.g., added or inserted) by application ofelectrical energy, or decreased by extraction of electrical energy, viaa motor-generator that is operably coupled to and/or otherwise includedin the primary energy storage portion of the device. One way to increaseenergy per unit mass of a flywheel is to form the flywheel, at least inpart, from high-strength, low density composite material (e.g., carbonfiber. Because carbon fiber has a higher tensile strength per unit massthan other materials (such as glass fiber or steel), a flywheel formedfrom carbon fiber can rotate at a relatively higher rotational velocity(due to higher tensile strength to resist circumferential stresses) fora given amount of mass, thus increasing the rotational kinetic energyfor that amount of mass, i.e. density per unit mass. However, compositematerials, such as those formed from carbon fiber, have much lowerstrength in the radial direction than in the circumferential directionbecause radial stresses are carried by the composite's matrix material,e.g. a polymer resin. The matrix material has much lower tensilestrength than the fiber material (e.g. carbon fiber). Thus, therotational velocities of flywheels formed of carbon fiber are limited bythe strength of the matrix, rather than the strength of the carbonfiber.

Thus, a need exists for devices and methods for changing therelationship between radial and circumferential stresses in flywheelsformed of high-strength composite materials to enable increased energyand/or power density of the flywheel.

SUMMARY

Apparatus and methods for force distribution in composite flywheelenergy storage systems are described herein. In some embodiments, anapparatus includes a hollow cylindrical flywheel for a motor/generator.The flywheel is formed of a composite material including a matrixmaterial and fibers oriented at least in part in a circumferentialdirection around the flywheel and embedded in the matrix material. Theflywheel has a radially inner surface, a radially outer surface, and aradial thickness between the radially inner surface and the radiallyouter surface. The flywheel is configured to rotate about a longitudinalaxis defined by the flywheel. The rotation of the flywheel generateshoop stress in the fibers in the circumferential direction andthrough-thickness stress in the matrix material in the radial direction.The material properties of the fibers and the matrix material are suchthat rotation of the flywheel about the longitudinal axis at a firstrotational velocity sufficiently high to produce structural failure ofthe flywheel produces failure of the matrix material in the radialdirection and not failure of the fibers in the circumferentialdirection. The apparatus further includes a plurality of load massesdistributed circumferentially around, and coupled to, the radially innersurface of the flywheel at a longitudinal segment along the longitudinalaxis such that rotation of the flywheel results in each load mass fromthe plurality of load masses producing a force in a radially outwarddirection on the radially inner surface. The force acts to reduce themaximum through-thickness stress in the matrix material such that asecond rotational velocity, greater than the first rotational velocity,sufficiently high to produce structural failure of the flywheel in thelongitudinal segment, produces failure of the fibers in thecircumferential direction and not failure of the matrix material in theradial direction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an electromagnetic machinestructure according to an embodiment.

FIG. 2 is a schematic illustration of an electromagnetic machinestructure according to another embodiment.

FIG. 2A is an enlarged schematic illustration of a portion of theelectromagnetic machine structure shown in FIG. 2 and identified as theregion labeled FIG. 2A.

FIGS. 3 and 4 are schematic illustrations of a portion of anelectromagnetic machine structure showing, for example, amotor/generator portion thereof, each according to a differentembodiment.

FIG. 5 is a cross-sectional perspective illustration of a flywheelaccording to an embodiment.

FIG. 6 is a cross-sectional perspective illustration of a flywheelaccording to another embodiment.

FIG. 7 is a perspective illustration of a stator assembly included inthe electromagnetic machine structure of FIG. 6.

FIG. 8 is a perspective illustration of a portion of a magnet assemblyconfigured to be disposed within the electromagnetic machine structureof FIG. 6.

FIG. 9 is a schematic illustration of a portion of the magnet assemblyof FIG. 7.

FIG. 10 is a schematic illustration of a portion of a magnetic assemblyaccording to an embodiment.

FIG. 11 is a cross-sectional perspective illustration of a flywheelaccording to another embodiment.

FIG. 12 is a top view of a portion of a magnet assembly configured to bedisposed within the electromagnetic machine structure of FIG. 11.

FIGS. 13-16 are graphs each illustrating a relationship between anamount of stress experienced by and a radius associated with anelectromagnetic machine structure under a different condition.

DETAILED DESCRIPTION

In some embodiments, an apparatus includes a hollow cylindrical flywheelfor a motor/generator. The flywheel is formed of a composite materialincluding a matrix material and fibers oriented at least in part in acircumferential direction around the flywheel embedded in the matrixmaterial. The flywheel has a radially inner surface, a radially outersurface, and a radial thickness between the radially inner surface andthe radially outer surface. The flywheel is configured to rotate about alongitudinal axis defined by the flywheel. The rotation of the flywheelgenerates hoop stress in the fibers in the circumferential direction andthrough-thickness stress in the matrix material in the radial direction.The material properties of the fibers and the matrix material are suchthat rotation of the flywheel about the longitudinal axis at a firstrotational velocity sufficiently high to produce structural failure ofthe flywheel produces failure of the matrix material in the radialdirection and not failure of the fibers in the circumferentialdirection. The apparatus further includes a plurality of load massesdistributed circumferentially around, and coupled to, the radially innersurface of the flywheel at a longitudinal segment along the longitudinalaxis such that rotation of the flywheel results in each load mass fromthe plurality of load masses producing a force in a radially outwarddirection on the radially inner surface. The force acts to reduce themaximum through-thickness stress in the matrix material such that asecond rotational velocity, greater than the first rotational velocityand sufficiently high to produce structural failure of the flywheel inthe longitudinal segment, produces failure of the fibers in thecircumferential direction and not failure of the matrix material in theradial direction.

In some embodiments, an apparatus includes a rotor configured to bedisposed within a flywheel energy storage device. The rotor is formed ofa composite material including a matrix material and fibers oriented atleast in part in a circumferential direction around the rotor embeddedin the matrix material. The rotor has a longitudinal axis of rotationand a radially inner surface. The rotor is configured to rotate aboutthe longitudinal axis relative to a stator. A first plurality of loadmasses and a second plurality of load masses are coupled to the innersurface of the rotor. Each load mass from the first plurality of loadmasses has a first density and a first size. A first portion of thefirst plurality of load masses is distributed along the inner surface inthe circumferential direction at a first longitudinal segment along theaxis of rotation, and a second portion of the first plurality of loadmasses is distributed along the inner surface in the circumferentialdirection at a second longitudinal segment along the axis of rotation.Each load mass from the second plurality of load masses has a seconddensity greater than the first density and a second size less than thefirst size. The second plurality of load masses is distributed along theinner surface in a circumferential direction at a third longitudinalsegment along the axis of rotation between the first longitudinalsegment and the second longitudinal segment. The first plurality of loadmasses and the second plurality of load masses cover the inner surfacesuch that a substantially uniform pressure is exerted on the innersurface of the rotor when the rotor is rotated about the longitudinalaxis relative to the stator.

In some embodiments, an apparatus includes a rotor configured to bedisposed within a flywheel energy storage device, a stator, and aplurality of load masses. The rotor is formed of a composite materialincluding a matrix material and fibers oriented at least in part in acircumferential direction around the rotor embedded in the matrixmaterial. The rotor includes a first plurality of magnets distributedalong an inner surface of the rotor in the circumferential direction ata first longitudinal segment along an axis of rotation defined by therotor. The rotor includes a second plurality of magnets distributedalong the inner surface in the circumferential direction at a secondlongitudinal segment along the axis of rotation. The first plurality ofmagnets and the second plurality of magnets define a space therebetween.The stator is disposed within the rotor such that a portion of thestator is within the space defined between the first plurality ofmagnets and the second plurality of magnets. A plurality of load massesare formed of a nonmagnetic material and are distributed along the innersurface in the circumferential direction and within the space definedbetween the first plurality of magnets and the second plurality ofmagnets such that the plurality of load masses is between the innersurface of the rotor and a circumferential surface of the portion of thestator. The first plurality of magnets, the second plurality of magnets,and the plurality of load masses collectively exert a substantiallyuniform pressure on the inner surface of the rotor operative in reducinga radial stress within the rotor when the rotor is rotated about thelongitudinal axis.

As used in this specification, the singular forms “a,” “an” and “the”include plural referents unless the context clearly dictates otherwise.Thus, for example, the term “a member” is intended to mean a singlemember or a combination of members, “a material” is intended to mean oneor more materials, or a combination thereof.

As used herein, the term “set” can refer to multiple features or asingular feature with multiple parts. For example, when referring to aset of walls, the set of walls can be considered as one wall withmultiple portions, or the set of walls can be considered as multiple,distinct walls. Thus, a monolithically constructed item can include aset of walls. Such a set of walls may include multiple portions that areeither continuous or discontinuous from each other. A set of walls canalso be fabricated from multiple items that are produced separately andare later joined together (e.g., via a weld, an adhesive, or anysuitable method).

As used herein, the term “substantially” when used in connection with ageometric relationship and/or characteristic (e.g., “cylindrical,”“linear,” “parallel,” “perpendicular,” etc.) is intended to convey thatthe structure so defined is nominally the geometric relationship and/orcharacteristic so defined. As one example, a portion of a surface of acomponent that is described as being “substantially linear” is intendedto convey that, although linearity of the surface is desirable, somenon-linearity can occur in the “substantially linear” surface. Suchnon-linearity can result from manufacturing tolerances, or otherpractical considerations (such as, for example, forces acting thereon).Thus, a geometric construction modified by the term “substantially”includes such geometric properties within a tolerance of, for example,plus or minus 5% of the stated geometric construction unless otherwiseexplicitly stated. For example, a “substantially linear” surface is asurface that defines a plane or an axis along a plane that is withinplus or minus 5% of being linear.

As used herein, the term “axial direction” can refer to, for example, adirection extending parallel to an axis of rotation of a component of anelectromagnetic machine. For example, in a motor/generator having arotor that is rotatably movable relative to a stator, a force can besaid to be in the axial direction when the force vector is substantiallyparallel a direction along an axis of rotation of the rotor.

As used herein, the term “rotational direction,” and/or “circumferentialdirection” can refer to, for example, a direction extending along asurface of a component having a fixed radius and in a direction ofrotation of the component (e.g., a component of a rotor included in amotor/generator). In considering, for example, a relatively smallportion of a component and/or a point along a surface of the component,a rotational direction can be considered a “tangential direction.”

As used herein, the term “radial direction” can refer to, for example, adirection extending, at a constant axial position, from an axis ofrotation of a component, for example, to an outer surface of thatcomponent. For example, a force can be said to be in the radialdirection when the force vector extends from an axis of rotation of arotor toward an outer surface of the rotor with a substantially fixedaxial position.

As used herein, the terms “tensile strength” and “shear strength” referto a materials ability to resist breaking under an applied force. Morespecifically, the term “tensile strength” refers to a material's abilityto resist breaking when subjected to a tensile or compressive force. Forexample, a material can be exposed to a tensile force when a firstportion of the material is pulled relative to a second portion of thematerial. The term “shear strength” refers to a material's ability toresist breaking when subjected to a shear force. For example, thematerial can be exposed to a shear force when the first portion of thematerial is pulled apart from the second portion of the material in aplanar direction (e.g., along a plane defined by the portion and thesecond portion).

As used herein, the term “tension” is related to the internal forces(i.e., stress) within an object in response to an external force pullingthe object in an axial direction. For example, an object with a massbeing hung from a rope at one end and fixedly attached to a support atthe other end exerts a force to place the rope in tension. The stresswithin an object in tension can be characterized in terms of thecross-sectional area of the object. For example, less stress is appliedto an object having a cross-sectional area greater than another objecthaving a smaller cross-sectional area. The maximum stress exerted on anobject in tension prior to plastic deformation (e.g., permanentdeformation such as, for example, necking and/or the like) ischaracterized by the object's tensile strength. The tensile strength isan intensive property of (i.e., is intrinsic to) the constituentmaterial. Thus, the maximum amount of stress of an object in tension canbe increased or decreased by forming the object from a material with agreater tensile strength or lesser tensile strength, respectively.

As used herein, the term “stiffness” is related to an object'sresistance to deflection, deformation, and/or displacement that isproduced by an applied force, and is generally understood to be theopposite of the object's “flexibility.” For example, a material with agreater stiffness is more resistant to deflection, deformation, and/ordisplacement when exposed to a force than a material having a lowerstiffness. Similarly stated, an object having a higher stiffness can becharacterized as being more rigid than an object having a lowerstiffness. Stiffness can be characterized in terms of the amount offorce applied to the object and the resulting distance through which afirst portion of the object deflects, deforms, and/or displaces withrespect to a second portion of the object. When characterizing thestiffness of an object, the deflected distance may be measured as thedeflection of a portion of the object different from the portion of theobject to which the force is directly applied. Said another way, in someobjects, the point of deflection is distinct from the point where forceis applied.

Stiffness (and therefore, flexibility) is an extensive property of theobject being described, and thus is dependent upon the material fromwhich the object is formed as well as certain physical characteristicsof the object (e.g., cross-sectional shape, length, boundary conditions,etc.). For example, the stiffness of an object can be increased ordecreased by selectively including in the object a material having adesired modulus of elasticity, flexural modulus, and/or hardness. Themodulus of elasticity is an intensive property of (i.e., is intrinsicto) the constituent material and describes an object's tendency toelastically (i.e., non-permanently) deform in response to an appliedforce. A material having a high modulus of elasticity will not deflectas much as a material having a low modulus of elasticity in the presenceof an equally applied stress. Thus, the stiffness of the object can beincreased, for example, by introducing into the object and/orconstructing the object of a material having a relatively high modulusof elasticity. As described in further detail herein, compositematerials (e.g., materials formed from two or more constituent materialshaving different physical or chemical properties) such as carbon fibercomposites generally increase the stiffness of a substrate material(e.g., plastic resin or glass) in a direction parallel to the directionof the carbon fibers.

Electromagnetic machines as described herein can be any suitable type ormachine used, for example, as an energy storage device, a motor, agenerator, and/or the like. By way of example, although some of theembodiments are described herein with reference to use within anelectromagnetic machine such as a flywheel or the like, it should beunderstood that the embodiments described herein can also be used withinother machines or mechanisms. Furthermore, while the embodiments aredescribed herein as being implemented in or on a flywheel including anintegrated motor/generator, it should be understood that the embodimentsdescribed herein can be implemented in or on a flywheel that is operablycoupled to a motor/generator and/or any other suitable electric,electromechanical, and/or electromagnetic device. While themotor/generators and/or other electromagnetic machines described hereinare generally permanent magnet electromagnetic machines such as axialflux machines and/or radial flux machines, the embodiments and/orcomponents thereof can be implemented in any suitable type of machine.

The embodiments described herein can be implemented in or on anelectromechanical flywheel configured to store energy in the form ofrotational kinetic energy. For example, energy (e.g., electric energy,mechanical energy, and/or the like) can be supplied to the flywheel,which results in rotation of a rotating mass (e.g., a rotor) about anaxis. Thus, the flywheel can store at least a portion of the energysupplied thereto. Conversely, energy can be discharged from the flywheelby reducing a rotational velocity of the rotor, for example, by inducingan electric current in the windings of a motor/generator, which in turn,delivers the electric current to a load.

Generally, it is desirable to increase the energy density (W-h/kg)associated with the flywheel while maintaining safe operatingconditions. Thus, in some instances, it is desirable to form rotatingcomponents of the flywheel (e.g., a rotor) from relatively lightweightand/or low-density materials. The stored rotational energy for a givensystem is represented by Equation 1 below:

$\begin{matrix}{E = {\frac{1}{2}I_{\omega^{2}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where E is energy, I is the mass moment of inertia, and ω is therotational velocity.

Thus, a flywheel energy storage device stores more energy as the massmoment of inertia I of the rotating parts and the rotational velocity ωis increased. The mass moment of inertia I for each individual componentthat is rotating is represented by Equation 2 below:

$\begin{matrix}{I = {\frac{1}{2}{m\left( {r_{o}^{2} + r_{i}^{2}} \right)}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where m is the rotating mass, r_(o) and r_(i) are the outer radius andinner radius, respectively, of the locations of each individual masscomponent.

Thus, the farther away a rotating mass is from its rotational axis, thelarger the mass moment of inertia and the higher the stored rotationalenergy for a given rotational velocity. While the energy stored by aflywheel is increased as the rotational velocity and size of therotating parts are increased, increasing the rotational velocityincreases the stresses within the constituent material. Specifically,rotational components of a flywheel are subject to circumferentialtensile stress (hoop stress) and through-thickness stress (radialstress). A component of the through-thickness stress, which varies withradius, is an internal stress in which a radially outer portion of thecomponent is pulled away from a radially inner portion (e.g., radialdeflection and/or radial deformation). Such internal stress results inrelatively high radially oriented tensile stress within the component.Thus, while it is generally desirable to use relatively lightweightmaterials to increase the energy per unit mass of a flywheel it is alsodesirable that the lightweight materials have, inter alia, high strengthproperties.

Accordingly, the embodiments described herein include a flywheel havinga rotor formed from high strength composite materials, i.e. materialswith a filament material embedded in a matrix material, in which thefilament materials have a relatively high tensile strength that cansustain relatively high circumferential, or hoop, stress. Although thedevices and methods are disclosed herein as including particularmaterials, any of the devices and methods described herein can useand/or can include any composite filament material, such as carbonfiber, Kevlar, glass fiber, high strength polyethylene fibers (e.g.,Dyneema® & Spectra®), basalt fibers, and/or nanometer carbon fibers toincrease the energy and/or power density of the flywheel per unit mass(e.g., by using materials with high tensile strength per unit mass).Specifically, in some embodiments, such carbon fiber can be, forexample, T1000g from Toray or IMS65 from Toho, which have tensilestrengths of 925,000 pounds per square inch (psi) and 870,000 psi,respectively. Composite materials, however, have a relatively lowability to resist failure due to tensile forces in the radial orthrough-thickness direction (e.g., radial deflection and/or deformation)because the high tensile strength filaments (e.g., carbon fibers) aregenerally oriented circumferentially. As a result, the otherconstituent(s) of the composite material (e.g., the polymeric matrixmaterial of a carbon fiber composite or the like) carry thethrough-thickness tensile stress. Thus, the embodiments described hereinare configured to mitigate the effect of through-thickness tensilestress on the constituent composite material forming at least a portionof the rotor of a flywheel while maintaining a high-energy storagedensity associated with the flywheel.

A discussion of the embodiments illustrated in FIGS. 1-12 is followed bya brief discussion of the mathematics and analytical results associatedwith the embodiments and/or methods described herein. It should beunderstood that the discussion of the theoretical and/or mathematicaljustification is presented by way of example to summarize one method ofanalysis and to provide a basis for the relevant principals; thediscussion is not intended to be a full explanation thereof. Rather, thediscussion of the theoretical and/or mathematical justification ispresented to provide context to the specific embodiments and methodsdescribed herein.

FIG. 1 is a schematic illustration of an electromagnetic machinestructure 100, according to an embodiment. The electromagnetic machinestructure 100 can be any suitable machine, system, or portion thereof.For example, the electromagnetic machine structure 100 includes aflywheel 105, a support structure 160, and at least one set of bearings162. As described in further detail herein, the flywheel 105 can be anysuitable device and/or assembly configured to store energy. For example,the flywheel 105 can be a device and/or system configured to storeenergy in the form of rotational kinetic energy.

The support structure 160 can be, for example, a hub, a housing, anaxle, etc. configured to support at least a portion of the flywheel 105.The bearing(s) 162 can be operably coupled between the support structure160 and the rotor 110 of the flywheel 105. In this manner, thebearing(s) 162 can allow at least a portion of the rotor 110 to rotaterelative to and/or otherwise about at least a portion of the supportstructure 160. In some embodiments, the bearing(s) 162 can be mechanicalbearings such as ball bearings, pin bearings, etc. In other embodiments,the bearing(s) 162 can be magnetic levitation, active or passivemagnetic stabilization bearings, gas bearings, or the like configured torotatably support a portion of the rotor 110 via magnetic and/or fluidic(gas) levitation or the like. In other embodiments, the bearing(s) 162can be a hybrid bearing (e.g., a mechanical/magnetic hybrid or thelike). As such, the support structure 160 and/or the bearing(s) 162support at least a portion of the rotor 110 to allow for rotationalmotion of at least a portion thereof.

In this embodiment, the flywheel 105 is an electromechanical device thatreceives energy from and/or delivers (discharges) energy to anelectrical load/source 170. The electrical load/source 170 can be, forexample, a utility, industrial, military, and/or any other suitable gridinfrastructure. In other embodiments, the electrical load/source 170 canbe, for example, any suitable commercial and/or residential electricalload/source. In addition, any suitable electrical conditioning deviceand/or system 172 can be electrically connected between the flywheel 105and the electrical load/source 170. Such electrical conditioning 172,for example, can change, alter, and/or otherwise condition a voltage,current, phase, frequency, and/or the like associated with the electricenergy received from the motor/generator 130.

As shown in FIG. 1, the flywheel 105 includes at least a rotor 110having a magnet assembly 120 and a stator assembly 140 having a set ofstator windings or coils (not separately shown in FIG. 1) thatcollectively form an integrated motor/generator 130 included in theflywheel 105. The flywheel 105 and/or the components thereof can haveany suitable arrangement and/or configuration, as described herein withreference to specific embodiments. For example, the flywheel 105 and/orthe motor/generator 130 can be an axial flux or radial flux permanentmagnet machine. In such embodiments, the rotor 110 of the flywheel 105can be rotated relative to the stator assembly 140 such that magneticflux associated with the rotation of permanent magnets included in themagnet assembly 120 induces a flow of electric current within the statorwindings of the stator assembly 140.

The flywheel 105 is configured to receive sufficient electric energyfrom the electrical load/source 170 to rotate the rotor 110 with adesired rotational energy and velocity, thereby transforming the inputpower (e.g., the electric energy) into kinetic energy associated withthe rotation of the rotor 110 relative to the stator assembly 140 (seee.g., Equations 1 and 2 above). For example, in some embodiments, therotational velocity associated with the rotor 110 can be between about1,000 revolutions per minute (rpm) and about 10,000 rpm, between about10,000 rpm and about 20,000 rpm, between about 20,000 rpm and about30,000 rpm, between about 30,000 rpm and about 40,000 rpm, between about40,000 rpm and about 50,000 rpm, or more. In at least one embodiment,the rotational velocity associated with the rotor 110 can be about36,000 rpm. The flywheel 105 is also configured to discharge at least aportion of the kinetic energy, for example, by inducing an electriccurrent to flow within a portion of the motor/generator 130 (e.g., thestator windings or coils included in the stator assembly 140), whichslows the rotational velocity of the rotor 110. Moreover, the rotor 110can be rotatably supported by the support structure 160 and thebearing(s) 162 with minimal losses (e.g., due to friction or the like)such that when the flywheel 105 is at steady state (e.g., the rotor 110is spinning with substantially constant velocity and the motor/generator130 is delivering little to no electric energy to the electricalload/source 170 or is electrically isolated therefrom), the flywheel 105“stores” the kinetic energy associated with the rotation of the rotor110.

In some embodiments, the rotor 110 can have a substantially annularcross-sectional shape. In other words, the rotor 110 has an innersurface, defining an inner radius of the rotor 110, and an outersurface, defining an outer radius of the rotor 110. The rotor 110 can beformed from composite materials such as those described above. Themagnet assembly 120 is configured to be coupled to the inner surface ofthe rotor 110. The magnet assembly 120 can include any number of magnetsthat are circumferentially arranged along the inner surface of the rotor110. In some embodiments, the circumferentially arranged magnets of themagnet assembly 120 can form a ring of magnets disposed at or on asegment of the inner surface along the longitudinal axis of the rotor110. In addition, the magnet assembly 120 can include any suitablenumber of magnet rings, each of which is disposed at a different segmentalong the longitudinal axis of the rotor 110.

The arrangement of the magnet assembly 120 is such that a space isdefined between each magnet ring and/or between axially adjacentmagnets. In some embodiments, the magnets included in and/orcollectively forming a ring of magnets can be segmented. That is to say,multiple magnets are arranged around the circumference of the innersurface to form the magnet ring with a substantially uniform spacedefined between each circumferentially adjacent magnet. In someembodiments, segmenting the magnets can, for example, reduce hoop,bending, and/or through-thickness stress within the magnets that couldotherwise result in failure. In addition, the amount of segmentation ofthe magnets of the magnet assembly 120 (e.g., a number of magnetsforming a circumferential ring of magnets) can at least partiallycontrol a frequency of the electric current associated with the rotationof the rotor 110 (e.g., the electric current delivered to the statorassembly 140 to rotate the rotor 110 or produced by the rotation of therotor 110 relative to the stator assembly 140). In some embodiments, theangular rotation of the rotor 110 and the segmentation of the magnets ofthe magnet assembly 120 can result in a relatively high frequency of theelectric current associated with the flywheel.

The stator assembly 140 can have a substantially circular (e.g., nothollow) or substantially annular cross-sectional shape. Moreover, thesize of the stator assembly 140 can be associated with, for example, theinner radius of the rotor 110, thereby allowing the stator assembly 140to be disposed within the rotor 110 with a desired air gap between atleast a portion of an outer surface of the stator assembly 140 and atleast a portion of an inner surface of the rotor 110 (e.g., a surfacehaving the inner radius). In some embodiments, the stator assembly 140can be coupled to the support structure 160 and/or to the fixed portionof the bearing(s) 162 such that the stator assembly 140 is maintained ina substantially fixed position while the rotor 110 rotates relativethereto.

The arrangement of the rotor 110 and the stator assembly 140 can be suchthat a portion of the stator assembly 140 is disposed within the spacedefined between axially adjacent magnets. For example, at least aportion of the stator windings (not shown in FIG. 1) can be disposedbetween the axially adjacent magnets (or the axially adjacent rings ofmagnets). Thus, a magnetic flux flowing within a flux flow path betweenand/or through the magnets included in the magnet assembly 120 isoperative to induce electric current in the stator windings of thestator assembly 140, as the rotor 110 is rotated relative thereto.Moreover, as described above, the electric energy transferred to and/orextracted from the flywheel 105 can have a relatively high frequencyelectric current (e.g., based on the angular velocity of the rotor 110and the segmentation of the magnets of the magnet assembly 120). Hence,the stator assembly 140 and/or the stator windings can be configured tominimize losses and/or heating associated with carrying the relativelyhigh frequency electric current and/or high inductance along theconductors of the stator windings (e.g., the conductors have a surfacearea sufficient to support the high frequency and/or high inductancewithout short circuiting and/or overheating).

In some embodiments, the axially adjacent magnets of the magnet assembly120 and the portion of the stator assembly 140 disposed therebetweencollectively form and/or collectively function as a portion of themotor/generator 130. Moreover, in some embodiments, the inner surface ofthe rotor 110 can include any suitable number of uniformly spacedmagnets and/or rings of magnets along a length of its axis. In someembodiments, the rotor 110 includes a number of uniformly spaced magnetsand/or rings of magnets along substantially the entire axial length ofthe rotor 110. Similarly, the stator assembly 140 can include a numberof portions having stator windings, each of which is disposed betweendifferent pairs of axially adjacent magnets. In other words, themotor/generator 130 can extend substantially the entire axial length ofthe flywheel 105. In some instances, increasing a portion of theflywheel 105 forming the motor/generator 130 can, for example, increasethe amount of energy stored by the flywheel 105 (e.g., increase energydensity) as well as the rate at which the flywheel 105 can charge ordischarge energy (e.g., increase power density).

In some embodiments, the electromagnetic machine structure 100 isconfigured to produce and/or otherwise be associated with energy storagehaving a high energy density. For example, as shown in Equations 1 and2, the energy E stored by the flywheel 105 is a function of therotational velocity ω of the rotor 110 and the mass moment of inertia Iof the rotor 110, which in turn, is a function of the mass m, the innerradius r_(i), and the outer radius r_(o) of the rotor 110. Thus, theenergy density associated with the flywheel 105 can be increased byincreasing at least one of the rotational velocity ω of the rotor 110,the mass m of the rotor 110, and/or the inner and outer radii r_(i) andr_(o) of the rotor 110. Moreover, as shown by Equations 1 and 2 above,the mass of the rotor 110 is a first order of magnitude variable whilethe rotational velocity of the rotor 110 is a second order of magnitudevariable. Therefore, the gain in rotational velocity of the rotor 110resulting from the increased strength per unit mass of the rotor 110(e.g., due to using composite materials), exponentially increases thekinetic energy associated with the rotor 110.

As shown in FIG. 1, the flywheel 105 includes a set of mass loads 132coupled to the inner surface of the rotor 110. The mass loads 132 can bemagnetic (e.g., the mass loads 132 form the magnets included in themagnet assembly 120) or can be inert (e.g., nonmagnetic) and distinctfrom the magnets included in the magnetic assembly 130. For example, insome embodiments, the mass loads 132 can form the magnets of the magnetassembly 120 and can, for example, induce a flow of electric current inthe stator windings of the stator assembly 140 and/or stabilize therotor 110 via a magnetic bearing arrangement.

In other embodiments, the mass loads 132 are formed from stainlesssteel, tungsten alloy, metal loaded polymers, and/or other nonmagneticmaterial. For example, the mass loads 132 can be disposed at discretepositions along the inner surface of the rotor 110. In otherembodiments, the mass loads 132 can cover the inner surface of the rotor110 substantially in its entirety. Moreover, the mass loads 132 can havea relatively high density and thus, can have a smaller size whilemaintaining the same mass. Similarly, the mass loads 132 can have a massper unit area on the inner surface of the rotor, and or a density, thatis substantially equal to that of the magnets in the magnet assembly 120and/or in a magnetic stabilization system. Thus, when the mass loads 132and the magnets of the magnet assembly 120 cover the inner surface ofthe rotor 110 substantially in its entirety, the mass loads 132 andmagnets of the magnet assembly 120 exert a substantially uniform forceon the inner surface of the rotor 110 as the rotor 110 rotates about itsaxis. In some embodiments, the mass loads 132 are segmented intostructurally discrete elements, and optionally such that a desireddistance is defined between adjacent magnets—in either a circumferentialdirection or an axial direction. By segmenting the mass loads 132, thestresses exerted on and/or in the mass loads 132 resulting from thecentrifugal effects of the rotor's rotation can be reduced. In addition,segmenting the mass loads 132 can allow for increased scalability.

The arrangement of the mass loads 132 on the inner surface of the rotor110 results in a different stress state than the stress state otherwiseassociated with the rotor 110 while it is rotating. For example, themass loads 132 are configured to exert an additional force on the innersurface of the rotor 110 as a result of centrifugal effects associatedwith the rotation of the rotor 110. As such, the maximumthrough-thickness radial tensile stress otherwise limiting therotational velocity of the rotor 110 is reduced. More specifically, theforce exerted by the mass loads 132 on the inner surface of the rotor110 can, in some instances, place the rotor 110 (or the constituentmaterial forming the rotor 110) in a compressive through-thicknessstate, which is desired due to the composite material's strength underthrough-thickness compression compared to through-thickness tension. Inaddition, the uniformity of the force exerted on the inner surface ofthe rotor 110 can stabilize non-uniform dynamic loading associated withincreasing and/or decreasing the rotational velocity of the rotor 110.

FIG. 2 is a schematic illustration of a mass loaded composite rotor 210according to an embodiment. In some embodiments, the mass loadedcomposite rotor 210 (also referred to herein as “rotor”) can be anysuitable rotor configured to be included in a flywheel energy storagedevice such as, for example, the flywheel 105 described above withreference to FIG. 1. As such, the rotor 210 can be configured to rotateabout an axis A relative to a stator assembly (not shown in FIG. 2). Asdescribed above with reference to the rotor 110, the rotor 210 can becaused to rotate to, for example, store energy in the form of rotationalkinetic energy. Moreover, the rotation of the rotor 210 relative to astator assembly (e.g., the stator assembly 140) can be such thatmagnetic flux associated with the rotation of permanent magnets includedin and/or coupled to the rotor 210 induces a flow of electric currentwithin the stator windings of the stator assembly 140.

The rotor 210 can be any suitable shape, size, and/or configuration. Forexample, in some embodiments, the rotor 210 has a substantially annularshape within which at least a portion of a stator assembly or the likecan be disposed. The rotor 210 can be formed from composite materialssuch as those described above. More specifically, as shown in FIG. 2,the rotor 210 includes a composite layer 212 and, optionally, acompliant layer 216. The composite layer 212, for example, can be formedof a high-strength carbon fiber composite. The composite layer 212includes a polymeric matrix material 215 such as, for example, epoxyresin or the like with carbon fibers 217 embedded therein. In suchembodiments, the carbon fibers 217 can be arranged and/or orientedsubstantially in a circumferential direction. As described above, thecomposite layer 212 can provide relatively high strength properties witha relatively low density, thereby increasing the strength of the rotor210 and a rate at which the rotor 210 can rotate before failure due tocentrifugal effects.

As shown in FIG. 2, the optional compliant layer 216 is disposed withinthe composite layer 212, in contact with and coupled to (e.g., via achemical or mechanical coupling) the inner surface of the compositelayer 212. The compliant layer 216 can be formed of a generallycompliant material having a lower modulus of elasticity than thecomposite layer 212. For example, in some embodiments, the compliantlayer 216 is formed of a glass or glass composite. As described infurther detail herein, the compliant layer 216 can be configured todistribute a force F otherwise exerted on the composite layer 212 toreduce, for example, localized stress concentrations.

The rotor 210 further includes one or more sets of mass loads 232coupled to an inner surface of the compliant layer 216. The mass loads232 can be magnetic and/or can be inert (e.g., nonmagnetic). Forexample, in some embodiments, the mass loads 232 can be magnets includedin a magnet assembly of a flywheel. The mass loads 232 can have arelatively high density when compared, for example, to the compliantlayer 216 and/or the composite layer 212. As shown in FIG. 2, each setof mass loads 232 is circumferentially arranged, and the sets of massloads are uniformly distributed along a length of the rotor 210 parallelto the axis A. In embodiments in which stator windings are disposedaxially between adjacent sets of magnetic mass loads 232, the axiallyadjacent sets of mass loads 232 are axially spaced to receive the statorwindings.

While the mass loads 232 are shown in FIG. 2 as defining a spacetherebetween, in other embodiments, the rotor 210 can include mass loads232 configured to cover substantially the entire inner surface of therotor 210 (i.e. the compliant layer 216 if included, or the compositelayer 212 if the compliant layer 216 is not included). For example, insome embodiments, a first portion of the mass loads 232 can be magneticmass, which can be substantially similar in form and/or function to themagnets included in the magnet assembly 120 described above in detailwith reference to FIG. 1. In such embodiments, a second portion of themass loads 232 can be disposed, for example, between the axiallyadjacent magnetic mass loads 232. In some embodiments, the secondportion of the mass loads 232 can have substantially the same density asthe first portion of the mass loads 232 or can have a greater densitythan the first portion of the mass loads 232. When the mass loads 232(e.g., the first portion and the second portion of the mass loads 232)cover the inner surface of the compliant layer 216 substantially in itsentirety, the mass loads 232 exert a substantially uniform force F perunit area on the inner surface of the compliant layer 216 as the rotor210 rotates about the axis A. As described above, the arrangement of thecompliant layer 216 is such that the otherwise localized force F perunit area exerted by the mass loads 232 on the compliant layer 216 isuniformly distributed on the inner surface of the composite layer 212.Thus, as the rotor 210 is rotated about the axis A, a substantiallyuniform stress is exerted (e.g., via the compliant layer 216) on theinner surface of the composite layer. In some instances, such anarrangement can, for example, increase a dynamic stability of theoverall rotor system.

As described above with reference to the rotor 110, the mass loads 232exert an additional force on the inner surface of the composite layer212 as a result of centrifugal effects associated with the rotation ofthe rotor 210. As such, the force F uniformly exerted by the mass loads232 on the inner surface of the composite layer 212 (via the compliantlayer 216) reduces through-thickness tensile radial stress otherwiselimiting the rotational velocity of the rotor 210. The force F can, insome instances, place the rotor 210 (or the constituent material formingthe rotor 210) in a compressive through-thickness state throughout therotor. Moreover, as described above with reference to the flywheel 105,by uniformly distributing the mass loads 232 (e.g., magnetic mass loads)the energy density and/or power density of a flywheel within which therotor 210 is included can be increased by substantially maximizing aportion of the flywheel collectively forming and/or configured as amotor/generator.

FIG. 3 is a schematic illustration of a portion of a flywheel 305according to another embodiment. The portion of the flywheel 305 can beincluded in any suitable machine and/or system configured to receive,store, and discharge energy. In some embodiments, the portion of theflywheel 305 can be substantially similar to and/or included in, forexample, the flywheel 105 described above with reference to FIG. 1.Thus, aspects of the portion of the flywheel 305 are not described infurther detail herein.

The flywheel 305 (or portion thereof) includes a rotor 310 configured torotate relative to a stator 340, as described above with reference tothe flywheel 105. The stator 340 can be any suitable shape, size, orconfiguration. For example, in some embodiments, the stator 340 can besubstantially similar to the stator assembly 140 described above withreference to FIG. 1. Therefore, although not shown in FIG. 3, the stator340 can include any number of stator windings or the like configured toreceive a flow of electric current, as described in further detailherein.

The rotor 310 of the flywheel 305 includes a first layer 312, a secondlayer 314, and a third layer 316. The first layer 312 can be ahigh-strength composite layer such as, for example, a carbon compositelayer, as described above with reference to the rotor 110 (FIG. 1)and/or the rotor 210 (FIG. 2). The second layer 314 can be a compositelayer having a strength that is less than the strength of the firstlayer 312. For example, in some embodiments, the second layer 314 can bea glass/carbon composite layer or the like. In such embodiments, theglass/carbon fibers can be embedded in a polymeric matrix material suchas, for example, epoxy resin. Thus, the second layer 314 can be similarto the first layer 312; however, the use of glass fibers results in amore compliant composite material when exposed to a force. The thirdlayer 316 can be a compliant layer having a strength that is less thanthe strength of the second layer 314. For example, in some embodiments,the third layer 316 can be a compliant glass layer, or glass compositelayer or the like. In such embodiments, the glass material and/or glasscomposite material can be more compliant, for example, than theglass/carbon composite and/or the carbon composite when exposed to aforce.

As shown in FIG. 3, the rotor 310 includes a magnet assembly 320 and aset of mass loads 332 coupled to a surface of the third layer 316 (e.g.,the glass layer). The magnet assembly 320 includes two sets of magnets322. The sets of magnets 322 can be coupled to the third layer 316 viaany suitable coupling such as, for example, an adhesive, a mechanicalfastener, an interference fit, an intervening structure attached to thethird layer 316, and/or the like. Moreover, the sets of magnets 322 arecoupled to the third layer 316 at different positions along an axiallength of the rotor 310 such that a distance D₁ is defined therebetween.As shown, the distance D₁ is sufficient to allow a portion of the stator340 to be disposed between the magnets 322.

The mass loads 332 can be any suitable shape, size, and/orconfiguration. For example, in the embodiment illustrated in FIG. 3, therotor 310 includes a set of mass loads 332 coupled to the third layer316 on each side of each of the sets of magnets 322. More specifically,a first set of mass loads 332 can be disposed on a first side of a firstset of magnets 322, a second sets of mass loads 332 can be disposed on afirst side of a second set of magnets 322, and a set of third mass loads332 can be disposed on a second side of the first set of magnets 322 anda second side of the second set if magnets 322 (i.e. axially between thetwo sets of magnets 322). In some embodiments, the sets of mass loads332 can be disposed adjacent to and in contact with one or more magnets322. In other words, the sets of magnets 322 and the sets of mass loads332 can substantially cover an inner surface of the third layer 316substantially in its entirety. As described in further detail herein, bycovering substantially the entirety of the inner surface of the thirdlayer 316, the sets of mass loads 332 and the sets of magnets 322 canexert a substantially uniform pressure on the third layer 316 as therotor 310 rotates about its axis.

In this embodiment, the each mass load in the sets of mass loads 332 canbe formed of an inert (e.g., nonmagnetic) material such as, for example,stainless steel, tungsten alloy, and/or the like. Moreover, theconstituent material forming the mass loads can be a relativehigh-density material. For example, in some embodiments, the mass loadsand/or the constituent material forming the mass loads in the set ofmass loads 332 have a density greater than a density of the magnets inthe sets of magnets 322. As shown in FIG. 3, by including mass loadswith a density greater than a density associated with the magnets, thesize (e.g., radial thickness) of the mass loads can be less than anassociated size of the magnets while maintaining substantially the samemass.

As described above, a portion of the stator 340 is disposed in the spacedefined between the sets of magnets 322. More specifically, the portionof the stator 340 can be centered in the axial direction between thesets of magnets 322 such that a distance D₂ is defined between oppositesurfaces of the stator 340 and an associated surface of the respectiveset of magnets 322, as shown in FIG. 3. Furthermore, the arrangement ofthe rotor 310 is such that a distance D₃ is defined between a radiallyouter surface of the stator 340 and a radially inner surface of the massload 332 disposed between the magnets 322. In some embodiments, distanceD₂ can be substantially the same as distance D₃, i.e. the same air gapcan be defined between the stator 340 and the sets of magnets 322 and/orsets of mass loads 332. This arrangement can, for example, increasestability of the portion of the flywheel 305 as the rotor 310 rotatesabout the stator 340.

As described above with reference to the flywheel 105 (FIG. 1) and theflywheel 205 (FIG. 2), the rotor 310 and the stator 340 collectivelyform an integrated motor/generator 330 included in the flywheel 305.More specifically, the arrangement of the portion of the stator 340disposed between adjacent sets of magnets 322 form, for example, anaxial flux permanent magnet motor/generator. Thus, the stator 340 canreceive a flow of electric current, which in turn, energizes the statorwindings. As such, the electric current flowing in or along the statorwindings can interact with the magnetic flux flowing between and/orthrough the adjacent sets of magnets 322 of the magnet assembly 320 torotate the rotor 310 relative to the stator 340. As such, the portion ofthe flywheel 305 can store at least a portion of the electric energy asrotational kinetic energy. In addition, the portion of the flywheel 305can be transitioned into, for example, a discharge state, in which themagnetic flux flowing between and/or through the sets of magnets 322induces a flow of an electric current within the stator windings to anelectric load or the like.

In some embodiments, the arrangement of the sets of mass loads 332 andthe sets of magnets 322 on the inner surface of the third layer 316results in a different stress state within each of the first layer 312,second layer 314, and third layer 316 of the rotor 310 than wouldotherwise be produced by rotation of the rotor 310. For example, as therotor 310 rotates about its axis, the sets of mass loads 332 and thesets of magnets 322 exert additional radially-outwardly-directed forceson the inner surface of the third layer 316 as a result of centrifugaleffects associated with the rotation of the rotor 310. As such, themaximum through-thickness radial tensile stress within the first layer312, second layer 314, and/or third layer 316 that would otherwise limitthe rotational velocity of the rotor 310 is reduced. In someembodiments, the force exerted by the sets of mass loads 332 and thesets of magnets 322 can place the layers 312, 314, and 316 of the rotor310 in an entirely compressive through-thickness state, as describedabove with reference to the flywheel 105 in FIG. 1. Moreover, by formingthe rotor 310 with layers 312, 314, and 316 that consecutively increasein strength as a function of the radius of the rotor 310, the forcesassociated with the centrifugal effects on the rotor 310, magnets 322,and mass loads 332 are uniformly distributed through the layers 312,314, and 316, which can stabilize non-uniform dynamic loading associatedwith increasing and/or decreasing the rotational velocity of the rotor310.

While the rotor 310 included in the portion of the flywheel 305 isparticularly shown and described above with reference to FIG. 3, inother embodiments, a portion of a flywheel can include a rotor havingany suitable arrangement and/or configuration. For example, FIG. 4 is aschematic illustration of a portion of a flywheel 405 according toanother embodiment. The portion of the flywheel 405 can be included inany suitable machine and/or system configured to receive, store, anddischarge energy. In some embodiments, the portion of the flywheel 405can be substantially similar to and/or included in, for example, theflywheel 105 described above with reference to FIG. 1. Furthermore,aspects of the portion of the flywheel 405 can be substantially similarin form and/or function to associated aspects of the portion of theflywheel 305. Thus, aspects of the portion of the flywheel 405 are notdescribed in further detail herein.

The flywheel 405 (or portion thereof) includes a rotor 410 configured torotate relative to a stator 440, as described above with reference tothe flywheel 105. The stator 440 can be any suitable shape, size, orconfiguration. For example, in some embodiments, the stator 440 can besubstantially similar to the stator assembly 140 described above withreference to FIG. 1. Therefore, although not shown in FIG. 4, the stator440 can include any number of stator windings or the like configured toreceive a flow of electric current, as described in further detailherein.

The rotor 410 of the flywheel 405 includes a first layer 412, a secondlayer 414, and a third layer 416. The first layer 412 can be ahigh-strength composite layer (e.g., a carbon composite layer or thelike), as described above with reference to the rotor 110 (FIG. 1)and/or the rotor 210 (FIG. 2). The second layer 414 can be a compositelayer having a strength that is less than the strength of the firstlayer 412 (e.g., a glass composite layer or the like), as describedabove with reference to the flywheel 305 shown in FIG. 3. The thirdlayer 416 can be a compliant layer having a strength that is less thanthe strength of the second layer 414 (e.g., a compliant glass or thelike), as described above with reference to the rotor 310 shown in FIG.3.

As shown in FIG. 4, the rotor 410 includes a magnet assembly 420 coupledto the third layer 416 (e.g., the compliant glass layer) and a set ofmass loads 432 coupled to, for example, a surface of the second layer414 (e.g., the glass composite layer). The magnet assembly 420 includesa pair of sets of magnets 422. The magnet assembly 420 is substantiallysimilar to the magnet assembly 320 described above with reference toFIG. 3 and thus, is not described in further detail herein. While thethird layer 316 of the rotor 310 was shown in FIG. 3 as extendingsubstantially the entire length of the portion of the rotor 310, in theembodiment shown in FIG. 4, the third layer 416 is disposed between themagnets 422 and the second layer 414 and not the mass loads 432 and thesecond layer 414. In some embodiments, limiting the third layer 416 tosegments along an axial length of the rotor 410 associated with the setsof magnets 422 can, for example, reduce the weight of the rotor 410while still mitigating the centrifugal effects on the sets of magnets422 and rotor 410 (e.g., shear stress, through-thickness stress, etc.).

The mass loads in the sets of mass loads 432 can be any suitable shape,size, and/or configuration. For example, in the embodiment illustratedin FIG. 4, the rotor 410 includes a set of mass loads 432 coupled to thesecond layer 414 on each side of each of the sets of the magnets 422,similar to the arrangement of the rotor 310 shown in FIG. 3. In thisembodiment, the sets of mass loads 432 are segmented, for example, intosmaller cross-sectional areas (e.g., in the radial plane) than anassociated cross-sectional area of the magnets 422. In some instances,segmenting the sets of mass loads 432 can be based, at least in part, onthe density of the mass loads and the associated stresses resulting fromthe rotation of the rotor 410. Thus, by reducing the cross-sectionalsize of each of the mass loads the stresses acting on or in the massloads as well as those acting on the rotor 410 can be reduced. Moreover,by segmenting the mass loads into smaller cross-sectional areas, forexample, can allow the mass loads to be coupled to the second layer 414of the rotor 410 without the third layer 416 being disposedtherebetween. In this manner, the portion of the flywheel 405 can besubstantially similar in at least function to any of the flywheels 105,205, and/or 305 described herein.

FIG. 5 is a cross-sectional illustration of a flywheel 505, according toan embodiment. The flywheel 505 can be any suitable machine, system, orportion thereof. For example, the flywheel 505 can be a device, machine,and/or system configured to store energy in the form of rotationalkinetic energy. In this manner, the flywheel 505 is an electromechanicaldevice that receives energy from and/or delivers (discharges) energy toan electrical load/source such as, for example, a utility, industrial,military, and/or any other suitable grid infrastructure. In otherembodiments, the electrical load/source can be, for example, anysuitable commercial and/or residential electrical load/source. In someembodiments, portions of the flywheel 505 can be similar to and/orsubstantially the same as associated portions of the flywheels 105, 205,305, and/or 405 described above and thus, portions of the flywheel 505similar to those previously described are not described in furtherdetail herein.

As shown in FIG. 5, the flywheel 505 includes at least a rotor 510having a magnet assembly 520 and multiple sets of mass loads 532, and astator 540 having a set of stator windings or coils (not shown in FIG.5). The flywheel 505 and/or the components thereof can have any suitablearrangement and/or configuration. For example, as shown in FIG. 5, aportion of the flywheel 505 can form a motor/generator 530 configured asan axial flux permanent magnet machine. In such embodiments, the rotor510 of the flywheel 505 can be rotated relative to the stator 540 suchthat magnetic flux associated with the rotation of permanent magnetsincluded in the magnet assembly 520 induces a flow of electric currentwithin the stator windings of the stator 540.

The flywheel 505 is configured to receive sufficient electric energyfrom the electrical load/source to rotate the rotor 510 with a desiredrotational velocity, thereby transforming the input energy (e.g., theelectric energy) into rotational kinetic energy (see e.g., Equations 1and 2 above), as described above with reference to the flywheel 105illustrated in FIG. 1. The flywheel 505 is also configured to dischargeat least a portion of the rotational kinetic energy, for example, byinducing an electric current to flow within a portion of themotor/generator 530 (e.g., the stator windings or coils included in thestator 540), which slows the rotational velocity of the rotor 510.

As shown in FIG. 5, the stator 540 has a substantially circular (e.g.,not hollow) cross-sectional shape that can be associated with, forexample, an inner surface of the rotor 510, thereby allowing the stator540 to be disposed within the rotor 510. In some embodiments, the stator540 can be coupled to any suitable support structure (not shown)configured to maintain the stator 540 in a substantially fixed positionwhile the rotor 510 rotates relative thereto. Moreover, the rotor 510and/or the stator 540 can include a bearing 562 disposed therebetweenconfigured to support at least a portion of the rotor 510 as it rotatesrelative to the stator 540. In some embodiments, the bearing 562 can be,for example, a static mechanical bearing such as a ball bearing or pinbearing. The stator 540 includes a bearing portion 542, a stabilizationportion 544, and a motor/generator portion 546 each of which isconfigured to interact with a portion different portion of the rotor510, as described in further detail herein.

As shown in FIG. 5, the rotor 510 has a substantially annularcross-sectional shape. In other words, the rotor 510 has an innersurface, defining an inner radius of the rotor 510, and an outersurface, defining an outer radius of the rotor 510. The rotor 510 can beformed from composite materials such as those described above. Moreover,while the rotor 510 is shown in FIG. 5 as including a single layerand/or is shown as being formed by a single composite material, in otherembodiments, the rotor 510 can include any suitable number of layers,which can each be formed of a different composite material. For example,in some embodiment, the rotor 510 can include three layers (e.g., ahigh-strength carbon composite outer layer, a glass/carbon compositemiddle layer, and a glass and/or glass composite inner layer, asdescribed above with reference to the rotors 310 and 410.

The magnet assembly 520 is coupled to the inner surface of the rotor510. The magnet assembly 520 can include any number of magnets that arecircumferentially arranged along the inner surface of the rotor 510, inone or more axially distributed sets of magnets. For example, as shownin FIG. 5, the magnet assembly 520 includes a set of bearing magnet(s)522, a set of stabilization magnet(s) 522′, and one or more sets ofmotor/generator magnet(s) 522″. The circumferentially arranged magnets(e.g., the bearing magnet(s) 522, the stabilization magnet(s) 522′, andthe motor/generator magnet(s) 522″) each can be one magnet or can be anysuitable number of segmented magnets. In some embodiments, segmentingthe magnets can reduce stresses within and/or otherwise exerted by themagnets during rotation of the rotor 510 (e.g., bending stresses, shearstresses, through-thickness stresses, hoop stresses, and/or the like),as described above with reference to the rotor 110 (FIG. 1). In someembodiments, the circumferentially arranged magnets of the magnetassembly 520 can form a ring of magnets disposed at or on a desiredsegment of the inner surface along a longitudinal axis of the rotor 510.For example, the set of bearing magnet(s) 522 can be disposed at a firstposition along the longitudinal axis, the set of stabilization magnet(s)522′ can be disposed at a second position along the longitudinal axisdifferent from the first position, and the one or more sets ofmotor/generator magnet(s) 522″ can be disposed at third and otherpositions along the longitudinal axis different from the first positionand the second position.

The bearing magnet(s) 522, the stabilization magnet(s) 522′, and themotor/generator magnet(s) 522″ (each of which is referred to henceforthas a single “magnet”) can be any suitable magnet. For example, in someembodiments, the magnets can be formed from rare earth metals such asneodymium-iron-boride, samarium-cobalt, aluminum-nickel-cobalt, and/orthe like. In other embodiments, the magnets can be electromagnets. Insome embodiments, the magnets included in the magnet assembly 520 can besubstantially similar (e.g., including substantially the sameconstituent material). In other embodiments, the magnets in the set ofbearing magnets 522, the set of stabilization magnets 522′, and/or theset(s) of motor/generator magnets 522″ need not be similar.

The set of bearing magnets 522 and the set of stabilization magnets 522′each can have any arrangement and/or configuration suitable in defininga desired magnetic flux flow path. For example, in some embodiments, theset of bearing magnets 522 can produce magnetic flux that interacts withthe bearing portion 542 of the stator 540. For example, in someembodiments, the magnetic flux flowing from and/or through the set ofbearing magnets 522 can repel and/or otherwise levitate a segment of thebearing portion 542 of the stator 540. As such, the set of bearingmagnets 522 and the bearing portion 542 of the stator 540 cancollectively act as a low friction bearing via magnetic levitation. Theset of stabilization magnets 522′ can produce magnetic flux thatinteracts with a stabilization portion 544 of the stator 540. As such,the set of stabilization magnets 522′ and the stabilization portion 544of the stator 540 can collectively stabilize the rotor 510 and/or stator540, for example, during acceleration or deceleration of the rotor 510.In some instances, the stabilization of the rotor 510 can reduce impactforces and/or non-uniform loading or motion that can otherwise damagethe rotor 510 and/or stator 540. Thus, the bearing 562, the set ofbearing magnets 522 and set of stabilization magnets 522′ of the rotor510, and the bearing portion 542 and stabilization portion 544 of thestator 540 collectively support and/or stabilize the rotor 510 as itrotates about the stator 540.

The set(s) of motor/generator magnets 522″ of the magnet assembly 520 isconfigured to interact with a motor/generator portion 546 of the stator540 to collectively define the motor/generator 530. While the set ofmotor/generator magnets 522″ is shown in FIG. 5 as having a continuouscross-sectional shape that defines, for example, three notches withinwhich a portion of the stator 540 is disposed, in other embodiments, theset of motor/generator magnets 522″ can include any suitable number ofsets of axially arranged magnets that collectively form themotor/generator magnet 522″. In other words, the set of motor/generatormagnets 522″ can have any arrangement and/or configuration suitable indefining a flow path in which magnetic flux flows between and/or throughthe set of motor/generator magnets 522″ to interact with at least aportion of the stator 540.

The arrangement of the rotor 510 and the stator 540 is such that themotor/generator portion 546 of the stator 540 is disposed within a spacedefined by the set of motor/generator magnets 522″. For example, in someembodiments, the set of motor/generator magnet 522″ defines a set ofnotches configured to receive the motor/generator portion 546 of thestator 540. In other embodiments, the set of motor/generator magnets522″ is formed by multiple sets of magnets that are axially arranged todefine a space between axially adjacent sets of magnets configured toreceive the motor/generator portion 546 of the stator 540. In someembodiments, the motor/generator portion 546 of the stator 540 caninclude, for example, stator windings and/or coils (not shown in FIG. 5)disposed within the notches and/or the space between the axiallyadjacent magnets (or the axially adjacent rings of magnets). Thearrangement of the set of motor/generator magnets 522″ of the rotor 510and the motor/generator portion 546 of the stator 540 is such that adesired air gap is defined therebetween. More specifically, thearrangement of the motor/generator portion 546 of the stator 540disposed between the set(s) of motor/generator magnets 522 collectivelyform, for example, an axial flux permanent magnet motor/generator (e.g.,the motor/generator 530). Thus, the flywheel 505 can be configured toreceive a flow of electric current operative to rotate the rotor 510relative to the stator 540 and/or can induce a flow of electric current(e.g., within the stator windings and/or coils), which can be deliveredto a load, as described in detail above with reference to the flywheels105, 205, 305, and/or 405.

As described above, the rotor 510 includes sets of mass loads 532. Thesets of mass loads 532 can be magnetic (e.g., the mass loads 532 formthe magnets included in the magnet assembly 520) or can be inert (e.g.,nonmagnetic) and distinct from the magnets included in the magneticassembly 530. For example, in some embodiments, the mass loads 532 canform the magnets of the magnet assembly 520 and can, for example, inducea flow of electric current in the stator windings of the stator 540and/or stabilize the rotor 510. In this embodiment, however, the sets ofmass loads 532 are formed from stainless steel, tungsten alloy, metalloaded polymers, and/or other nonmagnetic material. As shown in FIG. 5,the sets of mass loads 532 cover substantially the entire inner surfaceof the rotor 510 except for segments of the rotor 510 otherwise coveredby and/or coupled to the set of bearing magnets 522, set ofstabilization magnets 522′, and set(s) of motor/generator magnets 522″.

In some embodiments, each mass load in the sets of mass loads 532 canhave a mass and radially facing area that is substantially equal to amass of each of the magnets in the magnet assembly 520. Thus, when thesets of mass loads 532 and the sets of magnets 522, 522′, and 522″ ofthe magnet assembly 520 cover the inner surface of the rotor 510substantially in its entirety, the mass loads and magnets exert asubstantially uniform force per unit area (or pressure) on the innersurface of the rotor 510 as the rotor 510 rotates about its axis. Insome embodiments, the mass loads can have a density that is greater thana density of the magnets and thus, can have a smaller size (e.g., radialthickness) while maintaining the same mass (and, e.g., mass per unitarea). In some embodiments, each set of mass loads 532 is segmentedcircumferentially into structurally discrete mass loads, eithercircumferentially spaced, or abutting. Similarly, the sets of mass loads532 can be spaced axially such that a desired axial distance is definedbetween adjacent sets of magnets, or the sets of mass loads 532 can beabutting. By segmenting each set of mass loads 532, the stresses exertedon and/or in each individual mass load resulting from the centrifugaleffects can be reduced. Thus, the arrangement of the sets of mass loads532 and the magnet assembly 520 on the inner surface of the rotor 510results in a stress state associated with the rotation of the rotor 510that is different from the stress state otherwise associated withrotation of the rotor 510 without the sets of mass loads 532. As aresult, the rotational velocity of the rotor 510 can be increased, whichin turn, increases an energy and/or power density associated with theflywheel 505, as described in detail above with reference to at leastthe flywheels 105 (FIG. 1) and/or 205 (FIG. 2).

In some embodiments, a flywheel can be configured for high power storagedensity as well as high-energy storage density. For example, FIGS. 6-9illustrate a flywheel 605 (or portions thereof) according to anembodiment. The flywheel 605 can be any suitable machine, system, orportion thereof. For example, in some embodiments, the flywheel 605 isconfigured to receive electric energy to rotate a portion thereof at adesired rotational velocity, thereby transforming the electric energyinto rotational kinetic energy (see e.g., Equations 1 and 2 above) andis also configured to discharge at least a portion of the rotationalkinetic energy, for example, by inducing an electric current to flowfrom the flywheel 605 to an electric load (as described in detailabove). In some embodiments, portions of the flywheel 605 can be similarto and/or substantially the same as associated portions of the flywheels105, 205, 305, 405, and/or 505 described above and thus, portions of theflywheel 605 similar to those previously described are not described infurther detail herein.

As shown in FIG. 6, the flywheel 605 includes at least a rotor 610having a magnet assembly 620 and sets of mass loads 632, a stator 640having a set of motor/generator portions 646, and a hub 660. Theflywheel 605 and/or the components thereof can have any suitablearrangement and/or configuration. For example, as shown in FIG. 6, aportion of the flywheel 605 can form a motor/generator 630 configured asan axial flux permanent magnet machine. In such embodiments, the rotor610 of the flywheel 605 can be rotated relative to the stator 640 suchthat magnetic flux associated with the rotation of permanent magnetsincluded in the magnet assembly 620 induces a flow of electric currentwithin the stator windings of the stator 640. Moreover, the flywheel 605is arranged to store energy with a relatively high energy and powerdensity, as described in further detail herein.

As shown in FIGS. 6 and 7, the stator 640 has central structure 650 fromwhich the motor/generator portions 646 extend. The central structure 650(and thus, the stator 640) can have a substantially annularcross-sectional shape that can be associated with, for example, an innersurface of the rotor 610, thereby allowing the stator 640 to be disposedwithin the rotor 610. The central structure 650 defines a set ofopenings 652 configured to facilitate connecting the electrical wires tothe stator coils, but also reduces the weight of the stator 640 as wellas to allow access to portions of the flywheel 605 for serving, etc. Thestator 640 is fixedly coupled to the hub 660, which is configured tomaintain the stator 640 in a substantially fixed position while therotor 610 rotates relative thereto.

As shown in FIG. 7, each motor/generator portion 646 extends from thecentral structure 652 of the stator 640. The motor/generator portions646 can be substantially thin rings that include, for example, a set ofstator windings 648 (or coils). In some embodiments, the stator windings648 can be wound wires or the like. In other embodiments, the statorwindings 648 can be electrically conductive traces on, for example, aprinted circuit board. Although not shown in FIG. 7, the stator windings648 can be electrically coupled to any suitable device, load, system,grid, etc. such that electric current can flow therebetween. Asdescribed in further detail herein, the motor/generator portions 646 areconfigured to interact with the magnet assembly 620 of the rotor 610 tocollectively form the motor/generator 630 of the flywheel 605.

The rotor 610 has a substantially annular cross-sectional shape, asshown in FIG. 6. In other words, the rotor 610 has an inner surface,defining an inner radius of the rotor 610, and an outer surface,defining an outer radius of the rotor 610. The rotor 610 can be formedfrom composite materials such as those described above. While the rotor610 is shown in FIG. 6 as including a single layer and/or is shown asbeing formed by a single composite material, in other embodiments, therotor 610 can include any suitable number of layers, each of which canbe formed of a different composite material. For example, in someembodiments, the rotor 610 can include three layers (e.g., ahigh-strength carbon composite outer layer, a glass/carbon compositemiddle layer, and a glass and/or glass composite inner layer, asdescribed above with reference to the rotor 310 or the rotor 410.Moreover, the rotor 610 includes a bearing portion 618 configured toengage a bearing 662 of the hub 660. In some embodiments, the bearing662 can be, for example, a static mechanical bearing such as a ballbearing or pin bearing. In other embodiments, the bearing 662 can be amagnetic levitation bearing, an active or a passive magneticstabilization bearing, a gas bearing, and/or the like or a combinationthereof. Thus, the hub 660 and bearing 662 support the rotor 610 (via atleast the bearing portion 618) as the rotor 610 rotates relative to thehub 660 and stator 640.

The magnet assembly 620 is coupled to the inner surface of the rotor610. The magnet assembly 620 can include any number of sets of magnets622, each of which includes magnets that are circumferentially arrangedalong the inner surface of the rotor 610. The magnets in the sets ofmagnets 622 can be any suitable type of magnet such as those describedherein. In some embodiments, each of the sets of circumferentiallyarranged magnets of the magnet assembly 620 can be in the form of a ringof magnets 622, as shown, for example, in FIG. 8. For example, in someembodiments, the magnets in each set of magnets 622 can be coupled to anannular ring 624 configured to secure the magnets and to fixedly couplethe set of magnets 622 to the inner surface of the rotor 610.

Each of the circumferentially arranged rings of magnets 622 can includeany suitable number of segmented magnets. In some embodiments,segmenting the magnets can reduce stresses within and/or otherwiseexerted by the magnets during rotation of the rotor 610 (e.g., shearstresses, through-thickness stresses, hoop stresses, and/or the like),as described above with reference to the rotor 110 (FIG. 1). As shown inFIGS. 6 and 9, each of the circumferential rings of magnets 622 can bedisposed at or on a desired segment of the inner surface along alongitudinal axis of the rotor 610. For example, a first ring of magnets622 can be disposed at a first position along the longitudinal axis, asecond ring of magnets 622′ can be disposed at a second position alongthe longitudinal axis different from the first position, a third ring ofmagnets 622″ can be disposed at a third position along the longitudinalaxis different from the first position and the second position, and soforth.

The magnets 622 and/or the circumferential rings of magnets 622 can becoupled to the inner surface of the rotor 610 in any suitablearrangement. For example, as shown in FIG. 9, the magnets 622 can becoupled to the inner surface of the rotor 610 such that eachcircumferential ring of magnets 622 is separated from its axiallyadjacent circumferential rings of magnets 622 by a distance D₄.Similarly, each magnet 622 (e.g., segmented magnet) included in acircumferential ring of magnets 622 is separated from itscircumferentially adjacent magnets 622 by a distance D₅. As shown, themagnets can be arranged such that a magnet 622A having a polarity in afirst direction is circumferentially adjacent to magnets 622B having apolarity in a second direction opposite the first direction (and viceversa). Thus, a magnetic flux can flow between and/or through themagnets 622A and 622B within a predetermined magnetic flux flow path.

As shown in FIG. 9, the circumferential rings of magnets 622 can beoffset from their axially adjacent rings of magnets 622 by apredetermined angle. For example, each magnet 622A and 622B of the topring of magnets is coupled to the rotor 610 at a circumferentialposition along the inner surface; each magnet 622A and 622B of themiddle ring of magnets is coupled to the rotor 610 at a circumferentialposition along the inner surface that is offset from the magnets 622Aand 622B of the top ring; and each magnet 622A and 622B of the bottomring of magnets is coupled to the rotor 610 at a circumferentialposition along the inner surface that is offset from the magnets 622Aand 622B of the top ring and the magnets 622A and 622B of the middlering. In other embodiments, the magnets 622A and 622B need not beoffset. In other words, the circumferential rings of magnets 622 can bedistributed along the inner surface in the axial direction withsubstantially the same circumferential orientation.

Referring back to FIG. 6, the arrangement of the rotor 610 and thestator 640 is such that the motor/generator portion 646 of the stator640 is disposed within the space defined between the axially adjacentrings of magnets 622 (e.g., the space having the distance D₄ in FIG. 9).The arrangement of the rings of magnets 622 of the rotor 610 and themotor/generator portions 646 of the stator 640 is such that a desiredair gap is defined therebetween. More specifically, the arrangement ofthe motor/generator portion 646 of the stator 640 disposed between therings of magnets 622 collectively form, for example, an axial fluxpermanent magnet motor/generator (e.g., the motor/generator 630). Thus,the flywheel 605 can be configured to receive a flow of electric current(e.g., via the stator windings 648) operative to rotate the rotor 610relative to the stator 640 and/or can induce a flow of electric currentwithin the stator windings 648, which can be delivered to a load, asdescribed in detail above with reference to the flywheels 105, 205, 305,405, and/or 505.

As shown in FIG. 6, the magnets 622 and/or rings of magnets of the rotor610 and the motor/generator portions 646 of the stator are uniformlydistributed along substantially the entire length of the flywheel 605 inthe axial direction. Accordingly, the portion of the flywheel 605configured as the motor/generator 630 is increased and/or substantiallymaximized. As such, the power density of the flywheel 605 is increased,i.e., the rate at which the electric energy can be transferred to and/orfrom the flywheel 605 (via the stator windings 648) is increased. Forexample, if a stator winding 648 has a maximum electric capacity (e.g.,maximum voltage, current, and/or power that can be transferred along thestator winding 648 without failure), the electric power densityassociated with the flywheel 605 can be increased by increasing a numberof stator windings 648 included therein. Thus, increasing a portion ofthe flywheel 605 configured as the motor/generator 630 can result in theflywheel 605 having a high power density.

As described above, the rotor 610 includes the sets of mass loads 632.The sets of mass loads 632 can be magnetic (e.g., the sets of mass loads632 form at least a portion of the magnets 622 included in the magnetassembly 620) or can be inert (e.g., nonmagnetic) and distinct from thesets or rings of magnets 622 included in the magnet assembly 620. Inthis embodiment, the mass loads 632 are formed from stainless steel,tungsten alloy, metal loaded polymers, and/or other nonmagneticmaterial. In some embodiments, the mass loads 632 are segmented intostructurally discrete segments, and may be arranged such that a desireddistance is defined between adjacent magnets—in either a circumferentialdirection or an axial direction. By segmenting the mass loads 632, thestresses exerted on and/or in the mass loads 632 resulting from thecentrifugal effects can be reduced, as described above with reference tothe flywheels 105, 205, 305, 405, and/or 505.

As shown in FIG. 6, the sets of mass loads 632 are disposed within thespaces defined between the axially adjacent rings or sets of magnets 622(the space having the distance D₄ in FIG. 9). In some embodiments, eachof the mass loads 632 can have a mass that is substantially equal to amass of each of the magnets in the magnet assembly 620. Expandingfurther, a mass of each mass load 632 can be associated with and/ordependent on its position along the radius of the rotor 610 (e.g., amean radius of the mass). For example, when the sets of mass loads 632and the sets of magnets 622, 622′, and 622″ of the magnet assembly 620cover the inner surface of the rotor 610 substantially in its entiretyand have a substantially similar radial position (i.e., mean radius),the sets of mass loads 632 and sets of magnets 622, 622′, and 622″ ofthe magnet assembly 620 can have substantially the same mass. Thus, themass loads 632 and magnets can exert a substantially uniform pressure onthe inner surface of the rotor 610 as the rotor 610 rotates about itsaxis.

In other embodiments, each of the mass loads 632 can have a mass that isnot equal to a mass of each of the magnets in the magnet assembly 620,while nonetheless, collectively exerting the substantially uniformpressure on the inner surface of the rotor 610 as the rotor 610 rotatesabout its axis. For example, each of the mass loads 632 can have asmaller radial thickness or size than each of the magnets and thus, eachof the mass loads 632 can have a greater mean radius than a mean radiusassociated with each of the magnets included in the magnet assembly 620.In such embodiments, each mass load 632 can have a density that isgreater than a density of each of the magnets 622, 622′, and/or 622″ andthus, while having the smaller size (radial thickness), the mass loads632 and the magnets can exert a substantially uniform pressure loadingon the rotor 610. In this manner, each of the sets of mass loads 632 canbe disposed between the rotor 610 and a circumferential end surface ofthe corresponding one of the stator portions 646 while maintaining adesired air gap therebetween. Thus, the arrangement of the sets of massloads 632 and the magnet assembly 620 on the inner surface of the rotor610 results in a stress state associated with the rotation of the rotor610 that is different from the stress state otherwise associated withrotation of the rotor 610 without the mass loads 632. As a result, therotational velocity of the rotor 610 can be increased, which in turn,increases the energy and power density associated with the flywheel 605,as described in detail above with reference to at least the flywheels105 (FIG. 1) and/or 205 (FIG. 2).

While the magnets 622 are shown and described above as being coupled tothe rotor 610 via the annular ring 624, in other embodiments, magnetscan be coupled to a rotor via a magnet retention ring having anysuitable configuration. For example, FIG. 10 is a schematic view of aportion of a magnet assembly 720 according to an embodiment. The magnetassembly 720 can be included in and/or coupled to any suitable rotor orthe like such as the rotors 110, 210, 310, 410, 510, and/or 610described herein. In some embodiments, the magnet assembly 720 can becoupled to, for example, a composite layer 714 of a rotor (e.g., acarbon composite layer, a glass/carbon composite layer, and/or a glasscomposite layer, as described above with reference to the rotors 310(FIG. 3) and 410 (FIG. 4).

As shown in FIG. 10, the magnet assembly 720 includes a magnet retentionring 724 and a set of magnets 722 coupled thereto. The magnets 722 canbe any suitable magnets such as those described herein. The magnetretention ring 724 defines a set of notches 726 and a set of openings728. The notches 726 are configured to receive a portion of the magnets722 to fixedly couple the magnets to the magnet retention ring 724. Forexample, in some embodiments, the magnets 722 can be pressed into thenotches 726 and secured therein via an adhesive, a friction fit, amechanical fastener, a welded or sintered joint, and/or the like.

The openings 728 are configured to allow the magnet retention ring 724to deform when placed under a load. For example, in some embodiments,the magnetic retention ring 724 can deform as the magnets 722 arepressed into the openings 726. In some embodiments, the forces exertedon the magnet retention ring 724 due to the centrifugal effectassociated with the rotation of a rotor can be sufficient to deform aportion of the magnet retention ring 724. While the magnet retentionring 724 is shown as defining the openings 728, in other embodiments,the magnet retention ring 724 can define a slot, a notch, a groove, achannel, and/or any other suitable discontinuity configured to allow themagnet retention ring 724 to expand and/or to otherwise redistribute anamount of stress within the magnet retention ring 724 during loading.

The magnet retention ring 724 can be formed of a relatively compliantmetal, metal alloy, composite, and/or the like, with a relatively lowmodulus of elasticity. As such, a portion of the magnet retention ring724 can be configured to elastically (e.g., nonpermanently) expand inresponse to the stresses associated with the rotation of a rotor suchas, for example, radial stress and hoop stress. In some embodiments, theexpansion of the magnet retention ring 724 can result in a uniformdistribution of the individual forces exerted by each magnet 722. Thus,by expanding, the magnet retention ring 724 can exert a uniform force onan inner surface of the composite layer 714 of a rotor as the rotor isrotated about an axis. Moreover, by disposing the magnets 722 in thenotches 726 of the magnet retention ring 724, the shear stressassociated with the magnets 722 in response to angularacceleration/deceleration that would otherwise act to shear (e.g.,decouple) the magnets 722 from the inner surface of the rotor issupported by the magnet retention ring 724. By monolithically formingthe magnet retention ring 724, a surface area of the magnet retentionring 724 in contact with and coupled to the inner surface of the rotorcan provide a greater surface area over which the acceleration loads onthe magnets 722 can be carried by the inner surface of the rotor, i.e.reduce the magnitude of the shear stress for a given angularacceleration. As a result, changes in the rate of angularacceleration/deceleration of the rotor can be increased, which in turn,can increase a rate at which energy can be transferred to or from aflywheel within which such a rotor is disposed (i.e., increase a powerdensity of the flywheel).

While the flywheels 205, 305, 405, 505, and 605 have been shown anddescribed as being an axial flux permanent magnet machine, in otherembodiments, a flywheel configured to have a relatively high-energystorage density and/or a relatively high power density based at least inpart on mass loading can be any suitable type of electromagneticmachine. For example, FIGS. 11 and 12 illustrate a flywheel 805according to an embodiment. The flywheel 805 can be substantiallysimilar to the flywheels 105, 205, 305, 405, 505, and/or 605 describedherein in at least function. Thus, portions of the flywheel 805 are notdescribed in further detail herein.

As shown in FIG. 11, the flywheel 805 includes at least a rotor 810having a magnet assembly 820, a stator 840 having a set ofmotor/generator portions 846, and a hub 860. The stator 840 has centralstructure 850 configured to couple the stator 840 to the hub 860. Whilethe stator 640 is shown and described as having the motor/generatorportions 646 extending radially from the central structure 650, in theembodiment shown in FIGS. 11 and 12 the motor/generator portions 846 arearranged along a circumference of the central structure 850. Thus, thestator 840 is configured for use in a radial flux electromagneticmachine. As described above with reference to the stator 640, themotor/generator portions 846 of the stator 840 can include statorwindings such as, for example, wound wires or coils, electricallyconductive traces, and/or the like. As described in further detailherein, the motor/generator portions 846 are configured to interact withthe magnet assembly 820 of the rotor 810 to collectively form amotor/generator 830 of the flywheel 805.

The rotor 810 has a substantially annular cross-sectional shape with aninner surface and an outer surface. The rotor 810 can be formed fromcomposite materials such as those described above. While the rotor 810is shown in FIG. 11 as including a single layer and/or is shown as beingformed by a single composite material, in other embodiments, the rotor810 can include any suitable number of layers, which can each be formedof a different composite material. For example, in some embodiment, therotor 810 can include three layers (e.g., a high-strength carboncomposite outer layer, a glass/carbon composite middle layer, and aglass and/or glass composite inner layer, as described above withreference to the rotor 310 or the rotor 410. Moreover, the rotor 810includes a bearing portion 818 configured to engage a bearing coupled tothe hub 860. As such, the hub 860 rotatably supports the rotor 810 (viaat least the bearing portion 818) as the rotor 810 rotates relative tothe hub 860 and stator 840, as described above with reference to theflywheel 605.

The magnet assembly 820 is coupled to the inner surface of the rotor810. The magnet assembly 820 can include any number of magnets 822 thatare circumferentially arranged along the inner surface of the rotor 810.The magnets 822 can be any suitable type of magnet such as thosedescribed herein. In some embodiments, the circumferentially arrangedmagnets of the magnet assembly 820 can form a ring of magnets 822, asshown, for example, in FIG. 8. For example, in some embodiments, themagnets 822 can be coupled to magnet retention ring (not shown)configured to secure the magnets 822 and to fixedly couple the magnets822 to the inner surface of the rotor 810 (e.g., similar to the magnetretention ring 724 of FIG. 10).

Each of the circumferentially arranged rings of magnets 822 can be anysuitable number of segmented magnets 822. In some embodiments,segmenting the magnets 822 can reduce stresses within and/or otherwiseexerted by the magnets during rotation of the rotor 810 (e.g., shearstresses, through-thickness stresses, hoop stresses, and/or the like),as described above with reference to the rotor 110 (FIG. 1). As shown inFIG. 11, the circumferential rings of magnets 822 can be disposed at oron a desired segment of the inner surface along a longitudinal axis ofthe rotor 810 such that a circumferential ring of magnets 822 issubstantially aligned with a motor/generator portion 846 of the stator840.

As shown in FIG. 12, the magnets can be arranged such that each magnethas a polarity aligned in a desired direction. For example, a firstmagnet 822A has a polarity in a first circumferential direction; asecond magnet 822B is adjacent to the first magnet 822A and has apolarity in a first radial direction; a third magnet 822C is adjacent tothe second magnet 822B and has a polarity in a second circumferentialdirection opposite the first circumferential direction; and a fourthmagnet 822D is adjacent to the third magnet 822C and has a polarity in asecond radial direction opposite the first radial direction. Thecircumferential ring of magnets 822 can include any number of magnetsarranged with the same pattern of polarity. Thus, magnetic flux can flowbetween and/or through the magnets 822A, 822B, 822C, and 822D within apredetermined magnetic flux flow path. For example, in the embodimentshown in FIG. 12, the magnets 822 can be arranged in a Halbach array orthe like configured to direct a flow of magnetic flux, for example, in aradially inward direction while minimizing a flow of magnetic flux in aradially outward direction. This arrangement can obviate the need for aback iron or the like otherwise configured to define a magnetic fluxreturn path. As such, the magnetic flux flowing between and/or throughthe magnets 822 can interact with the motor/generator portion 846 of thestator 840 to produce an electromagnetic force operative to rotate therotor 810 relative to the stator 840 or to induce a flow of electriccurrent within the motor/generator portion 846 of the stator 840.

Although not shown in FIG. 11, the rotor 810 can include a set of massloads. The mass loads can be magnetic (e.g., the mass loads form atleast a portion of the magnets 822 included in the magnet assembly 820)or can be inert (e.g., nonmagnetic) and distinct from the magnets 822included in the magnet assembly 820. In some embodiments, the mass loadsare segmented such that a desired distance is defined between adjacentmagnets—in either a circumferential direction or an axial direction. Bysegmenting the mass loads, the stresses exerted on and/or in the massloads resulting from the centrifugal effects can be reduced, asdescribed above with reference to the flywheels 105, 205, 305, 405,and/or 505.

As described above, the mass loads can be disposed within the spacedefined between the axially adjacent magnets 822. In some embodiments,each of the mass loads can have a mass that is substantially equal to amass of each of the magnets in the magnet assembly 820 and thus, themass loads and the magnets of the magnet assembly 820 can exert asubstantially uniform pressure on an inner surface of the rotor 810. Inother embodiments, a mass and a mean radius of each mass load can bedifferent from a mass and a mean radius of each of the magnets in themagnet assembly 820. In other words, the mass loads can have a mass andradial thickness that is different from a mass and radial thickness ofeach of the magnets in the magnet assembly 820. Therefore, in suchembodiments, a substantially uniform pressure can be exerted on theinner surface of the rotor 810 by “tuning” and/or matching, for example,a product of the density, the radial thickness, and the localacceleration (where the local acceleration is equal to the product ofthe mean radius of the mass and the square of the rotational rate) orthe of masses and of the magnets. Thus, when the mass loads and themagnets 822 of the magnet assembly 820 cover the inner surface of therotor 810 substantially in its entirety, the mass loads and magnets 822of the magnet assembly 820 exert a substantially uniform pressure on theinner surface of the rotor 810 as the rotor 810 rotates about its axis.The arrangement of the mass loads and the magnet assembly 820 on theinner surface of the rotor 810 results in a stress state associated withthe rotation of the rotor 810 that is different from the stress stateotherwise associated with rotation of the rotor 810 without the massloads. As a result, the rotational velocity of the rotor 810 can beincreased, which in turn, increases an energy density associated withthe flywheel 805, as described in detail above with reference to atleast the flywheels 105 (FIG. 1) and/or 205 (FIG. 2).

Analysis and Results

As described above with reference to the specific embodiments, aflywheel energy storage device and/or system can include a rotorconfigured to rotate relative to a stator. The rotor of the flywheel canbe, for example, an annular cylinder considered as having a thin wall.The stresses within the rotor can be evaluated by considering thestress-strain relationships in the axial, radial, and tangential (hoop)direction. By evaluating at a given position along the rotational axis(e.g., assuming a unit axial thickness), the hoop stress and the radialstress at that given position can be equated in terms of theirstress-strain relationships, represented by Equation 3 below:

$\begin{matrix}{0 = {{\left( {\sigma_{h} - \sigma_{r}} \right)\left( {1 + v} \right)} + {r\left( {\frac{d\;\sigma_{h}}{dr} - {v\frac{d\;\sigma_{r}}{dr}}} \right)}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

where σ_(r) is the radial stress, σ_(h) is the hoop stress (also knownas the “circumferential tensile stress” or “tangential stress”), and νis Poisson's Ratio.

In use, the rotor of the flywheel rotates about its axis. Thecentrifugal effect associated with rotation produces a pressure on thewalls of the rotor, which can be evaluated, assuming unit axialthickness, in terms of the hoop stress and the radial stress, asrepresented by Equation 4 below:

$\begin{matrix}{{\sigma_{h} - \sigma_{r}} = {{\rho\; r^{2}\omega^{2}} + {r\frac{d\;\sigma_{r}}{dr}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

where ρ is the density of the material (e.g., density of the carboncomposite material forming the rotor), r is the radius of the rotor, andω is the rotational velocity.

By substituting Equation 4 into Equation 3 (and integrating,substituting, and simplifying), the radial stress and the hoop stressexerted on or in the rotor can be solved for as independent functions.Moreover, by considering the boundary conditions of the rotor at aninner radius and an outer radius as equaling zero, the radial stress andthe hoop stress exerted on or in the rotor can be expressed as twoseparate functions of a given radius and given rotational velocity, asrepresented, respectively, by Equations 5 and 6 below:

$\begin{matrix}{\sigma_{r} = {\frac{\left( {3 + v} \right)}{8}{{\rho\omega}^{2}\left\lbrack {R_{i}^{2} + R_{o}^{2} - \frac{R_{i}^{2}R_{o}^{2}}{r^{2}} - r^{2}} \right\rbrack}}} & {{Equation}\mspace{14mu} 5} \\{\sigma_{h} = {\frac{\left( {3 + v} \right)}{8}{{\rho\omega}^{2}\left\lbrack {R_{i}^{2} + R_{o}^{2} + \frac{R_{i}^{2}R_{o}^{2}}{r^{2}} - {\frac{\left( {1 + {3v}} \right)}{\left( {3 + v} \right)}r^{2}}} \right\rbrack}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

where R_(i) is the inner radius of the rotor and R_(o) is the outerradius of the rotor.

As described above, in some embodiments, a flywheel can include a rotorhaving any suitable number of discrete masses configured to exert aforce on an inner surface (i.e., inner radius) of the rotor as the rotorrotates about its axis. In some embodiments, the arrangement of themasses is such that a substantially uniform pressure is exerted on theinner surface of the rotor. The stress distribution resulting from thepressure associated with the mass loading produces, for example, aradial stress and a hoop stress on or in the rotor as a function of thepressure. The hoop stress resulting from the pressure produced by themass loading can be equated to the hoop stress resulting from therotational velocity of the rotor and thus, by substitution the radialstress and the hoop stress resulting from the mass loading can berepresented as a function of the rotational velocity and the radius ofthe rotor, as shown, respectively, by Equations 7 and 8 below:

$\begin{matrix}{\sigma_{r} = {{- \rho_{m}}r_{m}t\;\omega^{2}\frac{R_{i}^{2}}{R_{o}^{2} - R_{i}^{2}}\left( {1 - \frac{R_{o}^{2}}{r^{2}}} \right)}} & {{Equation}\mspace{14mu} 7} \\{\sigma_{h} = {\rho_{m}r_{m}t\;\omega^{2}\frac{R_{i}^{2}}{R_{o}^{2} - R_{i}^{2}}\left( {1 + \frac{R_{o}^{2}}{r^{2}}} \right)}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

where ρ_(m) is the density of each discrete mass, r_(m) is the meanradius of the discrete mass, t is the thickness of the discrete mass, ωis the rotational velocity of the rotor, r is a given radius of therotor, R_(i) is the inner radius of the rotor, and R_(o) is the outerradius of the rotor.

The effective pressure that a discrete mass exerts on the rotor,therefore, is represented by the leading terms in Equation 7 and 8, inwhich the effective mass loading pressure is equal to σ_(m)r_(m)tω². Asdescribed above, the effective mass loading pressure exerted by eachmass and by each magnet can be matched and/or uniformly distributed in aflywheel system such that a substantially uniform pressure acts on theinner surface of the composite rotor.

As shown by Equations 7 and 8, mass loading the inner surface of therotor can alter the stress state within a composite rotor as it rotates.In some instances, the mass loading of the composite rotor can result inplacing the composite rotor under radial compression rather than theradial tension otherwise resulting from centrifugal effects of rotation.Composite materials such as carbon fiber composites typically have veryhigh hoop stress failure limits and much lower radial stress failurelimits. Thus, composite rotors generally fail due to radial stress. Bymass loading the composite rotor, however, the composite rotor can beplaced in radial compression, which has a higher radial stress failurelimit when compared to its failure limit under radial tension (e.g., upto 20 times higher or more). Therefore, by placing the composite rotorunder radial compression the angular velocity associated with therotation of the rotor can be increased, which in turn, results in anincrease in energy and power storage density of the flywheel.

For example, FIGS. 13-16 illustrate graphs showing a stress state of acarbon composite rotor with mass loading and without mass loading. Inthese embodiments, the carbon composite can have a tensile radial stressfailure limit of about 5,000 pounds per square inch (psi) and atangential (hoop) stress failure limit of about 400,000 psi. The rotor,in these examples, has an inner radius of 7.5 inches (in.) and an outerradius of 12 in.

FIG. 13, for example, is a graph 1000 illustrating a radial stress inthe carbon composite rotor as a function of the rotor's radius (e.g.,between the inner radius of 7.5 in. and the outer radius of 12 in.). Asshown, the radial stress within composite rotor, when mass loaded andwhen rotating at 36,000 revolutions per minute (rpm), remains under the5,000 psi radial stress failure limit at each radial position betweenthe inner radius and the outer radius of the rotor. Conversely, theradial stress within the same composite rotor without mass loading andwhen rotating at the same 36,000 rpm exceeds the 5,000 psi failure limitbetween about 7.75 in. and about 11.5 in. This is consistent with theassumption that the rotor does not experience stress at the boundaryconditions (e.g., 7.5 in. inner radius and 12 in. outer radius. Asshown, by mass loading the composite rotor, the flywheel can produce orstore about 94 MegaJoules (MJ) of energy when rotating the compositerotor at about 36,000 rpm.

FIG. 14 is a graph 2000 illustrating a tangential (hoop) stress in thecarbon composite rotor as a function of the rotor's radius. Again, therotor is rotated with a rotational velocity of about 36,000 rpm. Asshown, the tangential stress is increased by mass loading the compositerotor; however, the tangential stress remains below the 400,000 psitangential stress failure limit for each radial position between theinner radius and the outer radius of the rotor.

FIG. 15 is a graph 3000 illustrating a radial stress in a carboncomposite rotor as a function of the rotor's radius without mass loadingthe composite rotor. As shown, the radial stress within the compositerotor without mass loading and when rotating at 19,000 revolutions perminute (rpm) remains under the 5,000 psi radial stress failure limit ateach radial position between the inner radius and the outer radius ofthe rotor. More specifically, the radial stress approaches the 5,000 psilimit at about the center of the rotor. Thus, without mass loading, thecomposite rotor approaches the 5,000 psi radial stress limit at 19,000rpm compared to 36,000 rpm when mass loaded. As a result, the flywheel,when rotated at 19,000 rpm, can produce or store only about 22.2 MJ ofenergy.

FIG. 16 is a graph 4000 illustrating a tangential (hoop) stress in thecarbon composite rotor as a function of the rotor's radius without massloading the composite rotor. Again, the rotor is rotated with arotational velocity of about 19,000 rpm. As shown, the tangential stresswithin the composite rotor remains far below the 400,000 psi tangentialstress failure limit for each radial position between the inner radiusand the outer radius of the rotor. More specifically, the maximumtangential stress remains below 100,000 psi, thus the rotor is gainslittle benefit from the high strength of the composite rotor in thetangential direction. Accordingly, as shown in FIGS. 13-16, mass loadinga composite rotor can allow the rotor to be rotated at highervelocities, which in turn, results in a higher energy storage densitywhen compared to a non-mass loaded composite rotor.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, notlimitation, and various changes in form and details may be made. Whereschematics and/or embodiments described above indicate certaincomponents arranged in certain orientations or positions, thearrangement of components may be modified. While the embodiments havebeen particularly shown and described, it will be understood thatvarious changes in form and details may be made.

Any portion of the apparatus and/or methods described herein may becombined in any combination, except mutually exclusive combinations. Theembodiments described herein can include various combinations and/orsub-combinations of the functions, components and/or features of thedifferent embodiments described. For example, a structure for anelectromagnetic machine can include a different quantity and/orcombination of magnets, masses, stator portions, etc. than shown withreference to specific embodiments.

In addition, it should be understood that the features, components andmethods described herein for each of the various embodiments can beimplemented in a variety of different types of electromagnetic machines,such as, for example, axial and radial machines that can supportrotational movement of a rotor assembly relative to a stator assembly.

Where methods and/or events described above indicate certain eventsand/or procedures occurring in certain order, the ordering of certainevents and/or procedures may be modified. Additionally, certain eventsand/or procedures may be performed concurrently in a parallel processwhen possible, as well as performed sequentially as described above.

What is claimed is:
 1. An apparatus, comprising: a hollow cylindricalflywheel for a motor/generator, the flywheel being formed of a compositematerial including a matrix material and fibers oriented at least inpart in a circumferential direction around the flywheel embedded in thematrix material, the flywheel having a longitudinal axis of rotation, aradially inner surface, a radially outer surface, and a radial thicknessbetween the inner surface and the outer surface, rotation of theflywheel about the axis of rotation generating hoop stress in the fibersin the circumferential direction and through-thickness stress in thematrix material in a radial direction, the material properties of thefibers and the matrix material being such that structural failure inresponse to rotation of the flywheel about the axis of rotation at afirst rotational velocity produces failure of the matrix material in theradial direction and not failure of the fibers in the circumferentialdirection; and a plurality of load masses distributed circumferentiallyaround, and coupled to, the inner surface of the flywheel at alongitudinal segment along the axis of rotation, each load mass from theplurality of load masses formed of an inert material, rotation of theflywheel causing each load mass from the plurality of load masses toproduce a radially outwardly directed force on the inner surface of theflywheel, the radially outwardly directed force acting to reduce amaximum through-thickness stress in the matrix material such thatstructural failure in response to rotation of the flywheel about theaxis of rotation at a second rotational velocity greater than the firstrotational velocity produces failure of the fibers in thecircumferential direction and not failure of the matrix material in theradial direction.
 2. The apparatus of claim 1, wherein each load massfrom the plurality of load masses has substantially the samecircumferential dimension, substantially the same axial dimension, andsubstantially the same radial dimension.
 3. The apparatus of claim 1,wherein each load mass from the plurality of load masses is configuredto maintain its structural integrity when the flywheel is rotated at thesecond rotational velocity.
 4. The apparatus of claim 1, wherein theplurality of load masses is a first plurality of load masses, thelongitudinal segment is a first longitudinal segment, and the radiallyoutwardly directed force is a first radially outwardly directed force,the apparatus further comprising: a second plurality of load massesdistributed circumferentially around, and coupled to, the inner surfaceof the flywheel at a second longitudinal segment along the axis ofrotation, rotation of the flywheel causing each load mass from thesecond plurality of load masses to produce a second radially outwardlydirected force on the inner surface of the flywheel, the second radiallyoutwardly directed force acting to reduce the maximum through-thicknessstress in the matrix material such that the matrix material does notfail in the radial direction along the second longitudinal segment atthe second rotational velocity.
 5. The apparatus of claim 4, whereineach load mass in the second plurality of load masses is formed of apermanent magnetic material.
 6. The apparatus of claim 4, wherein eachload mass in the second plurality of load masses is formed of an inertmaterial.
 7. The apparatus of claim 4, further comprising: a thirdplurality of load masses distributed circumferentially around, andcoupled to, the inner surface of the flywheel at a third longitudinalsegment along the axis of rotation, the third plurality of load massesbeing axially spaced from the second plurality of load masses to definean axial stator gap therebetween having a longitudinal gap length, eachload mass from the second plurality of load masses and each load massfrom the third plurality of load masses being formed of a permanentmagnetic material; and a stator having a plurality of conductivewindings disposed thereon and having an axial thickness less than thelongitudinal gap length, the stator being disposed in operativerelationship to the flywheel such that at least a portion of thewindings are disposed axially between the second plurality of loadmasses and the third plurality of load masses in the stator gap suchthat rotation of the flywheel relative to the stator produces a flow ofelectrical current in the windings.
 8. The apparatus of claim 7, whereinrotation of the flywheel causes each load mass from the third pluralityof load masses to produce a third radially outwardly directed force onthe inner surface of the flywheel, the third radially outwardly directedforce acting to reduce the maximum through-thickness stress in thematrix material such that the matrix material does not fail in theradial direction along the third longitudinal segment at the secondrotational velocity.
 9. The apparatus of claim 7, wherein each load massfrom the first plurality of load masses is disposed within the statorgap and radially between a radial surface of the stator and the innersurface of the flywheel.
 10. The apparatus of claim 9, wherein each loadmass from the first plurality of load masses has substantially the sameradial dimension, the radial dimension of each load mass from the firstplurality of load masses is a first radial dimension, and each load massfrom the second plurality of load masses and the third plurality of loadmasses has substantially the same radial dimension, the radial dimensionof each load mass from the second plurality of load masses and the thirdplurality of load masses is a second radial dimension greater than thefirst radial dimension.
 11. The apparatus of claim 10, wherein each loadmass from the first plurality of load masses has substantially the samedensity, the density of each load mass from the first plurality of loadmasses is a first density, and each load mass from the second pluralityof load masses and the third plurality of load masses has substantiallythe same density, the density of each load mass from the secondplurality of load masses and the third plurality of load masses is asecond density greater than the first density.
 12. The apparatus ofclaim 11, wherein each load mass from the first plurality of loadmasses, the second plurality of load masses and the third plurality ofload masses produces a substantially uniform pressure on the innersurface of the flywheel upon rotation of the flywheel.
 13. The apparatusof claim 4, wherein the first radially outwardly directed force issubstantially equal to the second radially outwardly directed force.